Mathematics 2: MAT14903 Summary
Blue = at formula sheet, yellow = important to remember
TIPS: spend time practicing the basic rules for calculating with the functions (discussed in Week 1). When you master
this, this will increase your chance of passing the exam significantly. Study all parts, including the mentioned
exercises, and focus also on the intermediate tests and practice exam, these tests represent the exam well.
Week 1: CH1 & CH2
Worked Exercises Tutorials and Review week 1
https://www.studeersnel.nl/nl/document/wageningen-university-research/mathematics-2/worked-exercises-
tutorials-and-review-week-1-mat-14903-i-mathematics-ii/19196345
Monday: Functions and derivatives
Polynomials
ABC:
2/1/0 Solutions
Rational functions has asymptotes → able to find
Power functions rules
1 1
𝑝
𝑥 = 𝑞 → 𝑥 = 𝑞 (𝑜𝑟 𝑥 = −𝑞 𝑖𝑓 𝑝 𝑖𝑠 𝑒𝑣𝑒𝑛)
𝑝 𝑝
𝟏
𝟐
Think of 𝒙𝟐 = √𝒙 = the same as 𝒙𝟐 since √𝒙𝟏
𝟏
= 𝒙−𝟐
𝒙𝟐
(𝟐𝒙)𝟐 = 𝟐𝟐 𝒙𝟐 (wanneer keer!)
𝒙𝟐 ∗ 𝒙𝟐 = 𝒙𝟐+𝟐
, 𝑞
𝑝 𝑞
𝑥 =𝑏 → 𝑥=𝑏 𝑝 !!!!!!!!!!!!!!!!!!!
𝟏 𝟑
𝒙𝟐 = 𝟐 → 𝒙 = 𝟐𝟐 thus 𝒙𝟐 = 𝒚𝟑 → 𝒙 = 𝒚𝟐
Inverse function
𝑔(𝑦) is the inverse function of 𝑓(𝑥)
Putting in 2 in 𝑓(𝑥)and then the answer into 𝑔(𝑦) is just a test for the inverse
The inverse is mirrored in the line 𝑦 = 𝑥
Exercise
1.9
A stimulus response relation is modelled with the function 𝑟(𝑠) = 2𝑠 0.3 . According to this model, find the factor by
which the stimulus should be increased to cause a response twice as large as the original one.
𝑠 0.3 = 2
1
𝑠 = 20.3 = 10.08
Answer: 10.08
,1.41D
Exponential and logarithmic functions
𝑓 (𝑥) = 𝑐 ∗ 𝑎 𝑥 𝑎 = the base, 𝑐= at 𝑦 = 0
ln(𝑥) 𝑖𝑠 𝑡ℎ𝑒 𝑖𝑛𝑣𝑒𝑟𝑠𝑒 𝑜𝑓 𝑒 𝑥
→ log and 10 power are inverse
Exercise 𝑙𝑛 (𝑥) & 𝑒 𝑥
, Back to functions
𝐥𝐨𝐠𝟏𝟎
𝟐𝒙 = 𝟏𝟎 → 𝒙 =
𝐥𝐨𝐠𝟐
alog(x) = log(x)/log(a)
*=+
/=-
^=*
10log (𝑞) → 𝑞
Counterparts for the same rules of the powers. P. 17
Blue = at formula sheet, yellow = important to remember
TIPS: spend time practicing the basic rules for calculating with the functions (discussed in Week 1). When you master
this, this will increase your chance of passing the exam significantly. Study all parts, including the mentioned
exercises, and focus also on the intermediate tests and practice exam, these tests represent the exam well.
Week 1: CH1 & CH2
Worked Exercises Tutorials and Review week 1
https://www.studeersnel.nl/nl/document/wageningen-university-research/mathematics-2/worked-exercises-
tutorials-and-review-week-1-mat-14903-i-mathematics-ii/19196345
Monday: Functions and derivatives
Polynomials
ABC:
2/1/0 Solutions
Rational functions has asymptotes → able to find
Power functions rules
1 1
𝑝
𝑥 = 𝑞 → 𝑥 = 𝑞 (𝑜𝑟 𝑥 = −𝑞 𝑖𝑓 𝑝 𝑖𝑠 𝑒𝑣𝑒𝑛)
𝑝 𝑝
𝟏
𝟐
Think of 𝒙𝟐 = √𝒙 = the same as 𝒙𝟐 since √𝒙𝟏
𝟏
= 𝒙−𝟐
𝒙𝟐
(𝟐𝒙)𝟐 = 𝟐𝟐 𝒙𝟐 (wanneer keer!)
𝒙𝟐 ∗ 𝒙𝟐 = 𝒙𝟐+𝟐
, 𝑞
𝑝 𝑞
𝑥 =𝑏 → 𝑥=𝑏 𝑝 !!!!!!!!!!!!!!!!!!!
𝟏 𝟑
𝒙𝟐 = 𝟐 → 𝒙 = 𝟐𝟐 thus 𝒙𝟐 = 𝒚𝟑 → 𝒙 = 𝒚𝟐
Inverse function
𝑔(𝑦) is the inverse function of 𝑓(𝑥)
Putting in 2 in 𝑓(𝑥)and then the answer into 𝑔(𝑦) is just a test for the inverse
The inverse is mirrored in the line 𝑦 = 𝑥
Exercise
1.9
A stimulus response relation is modelled with the function 𝑟(𝑠) = 2𝑠 0.3 . According to this model, find the factor by
which the stimulus should be increased to cause a response twice as large as the original one.
𝑠 0.3 = 2
1
𝑠 = 20.3 = 10.08
Answer: 10.08
,1.41D
Exponential and logarithmic functions
𝑓 (𝑥) = 𝑐 ∗ 𝑎 𝑥 𝑎 = the base, 𝑐= at 𝑦 = 0
ln(𝑥) 𝑖𝑠 𝑡ℎ𝑒 𝑖𝑛𝑣𝑒𝑟𝑠𝑒 𝑜𝑓 𝑒 𝑥
→ log and 10 power are inverse
Exercise 𝑙𝑛 (𝑥) & 𝑒 𝑥
, Back to functions
𝐥𝐨𝐠𝟏𝟎
𝟐𝒙 = 𝟏𝟎 → 𝒙 =
𝐥𝐨𝐠𝟐
alog(x) = log(x)/log(a)
*=+
/=-
^=*
10log (𝑞) → 𝑞
Counterparts for the same rules of the powers. P. 17
